The Sutton Local Studies & Archives covers Beddington, Carshalton, Sutton, Cheam, Wallington and the ancient parishes of Cuddington and Woodmansterne.
Here's the family history materials it contains:
https://www.sutton.gov.uk/info/200168/libraries_and_culture/1281/local_studies_and_archives/6
The Epsom and Ewell Local and Family History Centre covers the area around these two towns.
Read more at https://www.surreycc.gov.uk/heritage-culture-and-recreation/archives-and-history/local-history-centres-in-surrey-libraries/epsom-and-ewell-local-and-family-history-centre and http://www.epsomandewellhistoryexplorer.org.uk/EpsomHistoryCentre.html
There will be charges for any photocopies requested, postage if you want copies things sent to you, and bus fare (£3 per visit). No charge for digital photographs or emailing.
Please ask if you aren't sure what you're looking for! Many thanks, Lisa